scholarly journals New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp-Function Method

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hasibun Naher ◽  
Farah Aini Abdullah ◽  
M. Ali Akbar
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solutions ◽  
Traveling Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equation ◽  
Traveling Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions ◽  
Higher Dimensional

We construct new analytical solutions of the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.

scholarly journals The Probabilities of Obtaining Solitary Wave and Other Solutions in the Modified Noguchi Power Line

2021 ◽  
Vol 13 (4) ◽  
pp. 19
Author(s):  
Jean R. Bogning ◽  
Cédric Jeatsa Dongmo ◽  
Clément Tchawoua
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
Traveling Wave Solutions ◽  
Power Line ◽  
Partial Differential ◽  
Strongly Nonlinear ◽  
Wave Solutions

We use the implicit Bogning function (iB-function) to proceed to a kind of inventory of the possible solutions of the modified nonlinear partial differential equation which characterizes the modified power line of Noguchi. Firstly, we make an inventory of the forms of solutions through a field of possible solutions, then we identify the most probable forms that we set out to look for. The iB-function is used because it summarizes within it several types of different functions depending on the choice of its characteristics and it is easy to handle in the case of strongly nonlinear partial differential equations. In other words, we use the notion of probability to locate, through the characteristic indices of iB-functions, the forms of solitary and traveling wave solutions likely to propagate in the modified Noguchi power line.

Traveling Wave Solutions to the Burgers-αβ Equations

2016 ◽  
Vol 16 (1) ◽  
pp. 147-157 ◽  
Author(s):  
Byungsoo Moon
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Traveling Wave ◽  
Burgers Equation ◽  
Nonlinear Partial Differential Equation ◽  
Traveling Wave Solutions ◽  
Partial Differential ◽  
Decay Condition ◽  
Wave Solutions ◽  
Special Case

AbstractThe Burgers-αβ equation, which was first introduced by Holm and Staley [4], is considered in the special case where ${\nu=0}$ and ${b=3}$. Traveling wave solutions are classified to the Burgers-αβ equation containing four parameters ${b,\alpha,\nu}$, and β, which is a nonintegrable nonlinear partial differential equation that coincides with the usual Burgers equation and viscous b-family of peakon equation, respectively, for two specific choices of the parameter ${\beta=0}$ and ${\beta=1}$. Under the decay condition, it is shown that there are smooth, peaked and cusped traveling wave solutions of the Burgers-αβ equation with ${\nu=0}$ and ${b=3}$ depending on the parameter β. Moreover, all traveling wave solutions without the decay condition are parametrized by the integration constant ${k_{1}\in\mathbb{R}}$. In an appropriate limit ${\beta=1}$, the previously known traveling wave solutions of the Degasperis–Procesi equation are recovered.

scholarly journals Studying on Kudryashov-Sinelshchikov dynamical equation arising in mixtures liquid and gas bubbles

2021 ◽  
pp. 247-247
Author(s):  
Haci Baskonus ◽  
Adnan Mahmud ◽  
Kalsum Abdulrahman Muhamad ◽  
Tanfer Tanriverdi ◽  
Wei Gao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Function Method ◽  
Dynamical Equation ◽  
Nonlinear Partial Differential Equation ◽  
Gas Bubbles ◽  
Partial Differential ◽  
Wave Solutions

In this paper, some new exact traveling and oscillatory wave solutions to the Kudryashov-Sinelshchikov nonlinear partial differential equation are investigated by using Bernoulli sub-equation function method. Profiles of obtained solutions are plotted.

scholarly journals Explicit Exact Solutions of the (2+1)-Dimensional Integro-Differential Jaulent–Miodek Evolution Equation Using the Reliable Methods

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Supaporn Kaewta ◽  
Sekson Sirisubtawee ◽  
Nattawut Khansai
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solutions ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Transformation ◽  
Jacobi Elliptic Function ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Wave Solutions

In this article, we utilize the G′/G2-expansion method and the Jacobi elliptic equation method to analytically solve the (2 + 1)-dimensional integro-differential Jaulent–Miodek equation for exact solutions. The equation is shortly called the Jaulent–Miodek equation, which was first derived by Jaulent and Miodek and associated with energy-dependent Schrödinger potentials (Jaulent and Miodek, 1976; Jaulent, 1976). The equation is converted into a fourth order partial differential equation using a transformation. After applying a traveling wave transformation to the resulting partial differential equation, we obtain an ordinary differential equation which is the main equation to which the both schemes are applied. As a first step, the two methods give us distinguish systems of algebraic equations. The first method provides exact traveling wave solutions including the logarithmic function solutions of trigonometric functions, hyperbolic functions, and polynomial functions. The second approach provides the Jacobi elliptic function solutions depending upon their modulus values. Some of the obtained solutions are graphically characterized by the distinct physical structures such as singular periodic traveling wave solutions and peakons. A comparison between our results and the ones obtained from the previous literature is given. Obtaining the exact solutions of the equation shows the simplicity, efficiency, and reliability of the used methods, which can be applied to other nonlinear partial differential equations taking place in mathematical physics.

EXACT TRAVELING WAVE SOLUTIONS OF A HIGHER-DIMENSIONAL NONLINEAR EVOLUTION EQUATION

2010 ◽  
Vol 24 (10) ◽  
pp. 1011-1021 ◽  
Author(s):  
JONU LEE ◽  
RATHINASAMY SAKTHIVEL ◽  
LUWAI WAZZAN
Keyword(s):  
Traveling Wave ◽  
Function Method ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Periodic Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Higher Dimensional

The exact traveling wave solutions of (4 + 1)-dimensional nonlinear Fokas equation is obtained by using three distinct methods with symbolic computation. The modified tanh–coth method is implemented to obtain single soliton solutions whereas the extended Jacobi elliptic function method is applied to derive doubly periodic wave solutions for this higher-dimensional integrable equation. The Exp-function method gives generalized wave solutions with some free parameters. It is shown that soliton solutions and triangular solutions can be established as the limits of the Jacobi doubly periodic wave solutions.

scholarly journals Exact traveling wave solutions for a new nonlinear heat transfer equation

2017 ◽  
Vol 21 (4) ◽  
pp. 1833-1838 ◽  
Author(s):  
Feng Gao ◽  
Xiao-Jun Yang ◽  
Yu-Feng Zhang
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Linear Partial Differential Equation ◽  
Heat Transfer Equation ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Transfer Problems

In this paper, we propose a new non-linear partial differential equation to de-scribe the heat transfer problems at the extreme excess temperatures. Its exact traveling wave solutions are obtained by using Cornejo-Perez and Rosu method.

scholarly journals Exact solutions of (1+1)-Dimensional Kaup-Kupershmidt equation

2021 ◽  
Vol 12 (2) ◽  
pp. 3029-3031
Author(s):  
Anjali Verma, Et. al.
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solutions ◽  
Analytical Solutions ◽  
Nonlinear Partial Differential Equation ◽  
Partial Differential

In this paper, we have obtained new analytical solutions of Kaup-Kupershmidt equation by using one method. We conclude that One method present a wider applicability for managing nonlinear partial differential equation. The solutions obtained in this paper are new.

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